Exact Asymptotics in Channel Coding
Cornell University - Department of Electrical and Computer Engineering
Thursday, January 24, 2013|
4:00pm - 5:00pm
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About the Event
Information-theoretic results describing the limits of reliable communication over noisy channels are typically asymptotic in the block length. In practice, however, small block lengths are desirable and thus the speed of convergence of these characterizations is important. Classical results show that the error probability converges to zero exponentially fast with the block length if the data rate is fixed. But this exponent is very small in the regime of practical interest, so the subexponential "pre-factor" plays an important role. Yet very little is known about the pre-factor. Using techniques from probability theory, convex optimization. and information theory, we characterize the order of the pre-factor for all but a degenerate class of channels; for this class, the results tightly bound the order. These results provide the first order-improvement in pre-factor bounds in several decades. Time permitting, I will also discuss error probability estimates in the "moderate deviations" regime in which the rate approaches capacity and the error probability tend to zero simultaneously.
Aaron Wagner is an Associate Professor in the School of Electrical and Computer Engineering at Cornell University. He received the B.S. degree from the University of Michigan, Ann Arbor, and the M.S. and Ph.D. degrees from the University of California, Berkeley. During the 2005-2006 academic year, he was a Postdoctoral Research Associate in the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign and a Visiting Assistant Professor in the School of Electrical and Computer Engineering at Cornell. He has received the NSF CAREER award, the David J. Sakrison Memorial Prize from the U.C. Berkeley EECS Dept., the Bernard Friedman Memorial Prize in Applied Mathematics from the U.C. Berkeley Dept. of Mathematics, and teaching awards at the Department, College, and University level.
Contact: Ann Pace
Sponsor(s): University of Michigan
Open to: Public